Over what range will integer arithmetic addition and subtraction be accurate to the integer in IEEE double precision floating point?

Question

According to Wikipedia on the IEEE 64-bit floating point standard:

Between 2⁵²=4,503,599,627,370,496 and 2⁵³=9,007,199,254,740,992 the representable numbers are exactly the integers. For the next range, from 2⁵³ to 2⁵⁴, everything is multiplied by 2, so the representable numbers are the even ones, etc.

Does this mean contiguous integers can be represented up to 2⁵³?

In short I am trying to find the range of integer values upon which integer addition and subtraction operations will result in an exactly correct result.

Answer 1

Yes, all integers from -2⁵³ to +2⁵³, inclusive, are representable in IEEE-754 64-bit floating-point. An implementation that conforms to IEEE 754 will return exactly correct results for all operations a+b and a-b where a, b, and the mathematical result are integers in that interval.

Obviously, some results will be outside that interval, such as 2⁵³+1, so many operations that produce such results will produce a value that is not exact due to rounding to a representable value.

An interval such that a and b being integers in the interval guarantees that a+b and a-b are exact is -2⁵² to +2⁵², inclusive.